Energy and mass balance of Zhadang glacier surface, centralTibetan Plateau

Guoshuai ZHANG,1 Shichang KANG,1,2* Koji FUJITA,3 Eva HUINTJES,4 Jianqing XU,5

Takeshi YAMAZAKI,6 Shigenori HAGINOYA,7 Yang WEI,1 Dieter SCHERER,8

Christoph SCHNEIDER,4 Tandong YAO1,2

1Key Laboratory of Tibetan Environmental Changes and Land Surface Processes, Chinese Academy of Sciences, Beijing, ChinaE-mail: shichang.kang@itpcas.ac.cn

2State Key Laboratory of Cryospheric Sciences, Chinese Academy of Sciences, Lanzhou, China3Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan

4Department of Geography, RWTH Aachen University, Aachen, Germany5Japan Agency for Marine–Earth Science and Technology, Yokohama, Japan

6Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan7Meteorological Research Institute, Tsukuba, Japan

8Department of Ecology, Technical University of Berlin, Berlin, Germany

ABSTRACT. Climate variables that control the annual cycle of the surface energy and mass balance onZhadang glacier in the central Tibetan Plateau were examined over a 2 year period using a physicallybased energy-balance model forced by routine meteorological data. The modelled results agree withmeasured values of albedo, incoming longwave radiation, surface temperature and surface level of theglacier. For the whole observation period, the radiation component dominated (82%) the total surfaceenergy heat fluxes. This was followed by turbulent sensible (10%) and latent heat (6%) fluxes.Subsurface heat flux represented a very minor proportion (2%) of the total heat flux. The sensitivity ofspecific mass balance was examined by perturbations of temperature (��1K), relative humidity (�20%)and precipitation (�20%). The results indicate that the specific mass balance is more sensitive tochanges in precipitation than to other variables. The main seasonal variations in the energy balancewere in the two radiation components (net shortwave radiation and net longwave radiation) and thesecontrolled whether surface melting occurred. A dramatic difference in summer mass balance between2010 and 2011 indicates that the glacier surface mass balance was closely related to precipitationseasonality and form (proportion of snowfall and rainfall).

INTRODUCTIONAgainst the background of global warming, the variations ofglaciers in the Tibetan Plateau (TP) area and their effect onthe surrounding environment have drawn great attention(Immerzeel and others, 2010; Bolch and others, 2012).Accompanied by a significant temperature increase sincethe mid-19th century, the majority of glaciers on the TP haveretreated (e.g. Yao and others, 2004; Sakai and others, 2006;Ye and others, 2006). Numerical studies have shown thatglaciers in the TP have retreated with increasingly negativemass balance in recent years (e.g. Shi and Liu, 2000; Xiaoand others, 2007; Li and others, 2008; Bolch and others,2010). Glacial retreat and significant mass loss may not onlycause natural hazards such as landslides and glacier lakeoutburst floods but also endanger water resources in thelonger term (Immerzeel and others, 2010).

Investigations of the relationship between climate andglacier mass balance have been undertaken using variousempirical and physical models (e.g. Andreas, 1987;Braithwaite and Olesen, 1990; Kayastha and others, 1999;Hock, 2005). Physical models provide direct estimates ofenergy-balance components, but detailed observational dataare required for validation. Owing to the lack of obser-vational data for the TP, few studies have applied physical

models to investigate glacier surface energy and massbalance in the region. Observations of climate and massbalance for Zhadang glacier in the central TP have beenconducted since 2005 (Kang and others, 2009; Zhou andothers, 2010), providing an opportunity to test an energy-balance model for glacier energy and mass balance.Formulating a realistic physically based model of glaciermass balance is critical to predicting future glacier changeunder different climate projections, especially given thatvery few such studies have been undertaken in the TP(Takahashi and others, 1989; Zhang and others, 1996; Yangand others, 2011).

FIELD OBSERVATIONSZhadang glacier (Fig. 1) is on the northeastern slope ofNyainqentanglha mountain in the central TP (30828.570 N,90838.710 E; area 2.0 km2; length 2.2 km). This valley-typeglacier faces north-northwest and flows from 6090 to5515ma.s.l. It is debris-free and has a fan-shaped terminus(Chen and others, 2009). Two automatic weather stations(AWSs) have been operating at Zhadang glacier since May2005 (AWS1 at 5400ma.s.l. and AWS3 at 5800ma.s.l.;Fig. 1). An automatic energy-budget station which providesthe data for analysis located in the ablation zone has beenoperational since May 2009 (AWS2 at 5660m a.s.l.;Maussion and others, 2011). AWS2 measures the following

Journal of Glaciology, Vol. 59, No. 213, 2013 doi:10.3189/2013JoG12J152

*Present address: Institute of Tibetan Plateau Research, Chinese Academy ofSciences, Beijing, China.

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data every 10min for a nearly horizontal glacier surface:incoming and reflected solar radiation, air temperature,relative humidity, air pressure, net radiation (1.8m above theglacier surface), wind speed and wind direction (2.5m abovethe glacier surface) and surface temperature. Surface level ofthe glacier at AWS2 was measured by a sonic ranging sensor.At the glacier terminus (5580ma.s.l.), an all-weather raingauge with a hanging weighing transducer (T200b) has beenoperating since 21 May 2010 (Fig. 1). Details of the AWSsand rain gauge instruments are listed in Table 1.

The temperature and relative humidity sensors are inventilated radiation shields (THIES Clima GmbH). Theventilators are directly connected to two solar panels, whichprevent temperature errors introduced by radiation over-heating. Relative humidity measurements recorded whentemperature was below 08C and were corrected using themethod of Curry and Webster (1999). To avoid the effect of apoor cosine response of the radiation sensors at low sunangles, and a possible phase shift due to tilting of the sensorduring the daily cycle of incoming solar radiation (Giesenand others, 2009), the albedo (�), defined as the ratio of thereflected to the incident shortwave radiation, was calculatedusing the accumulated albedo method (Van den Broeke andothers, 2004).

AWS2 toppled over on 1 July 2009 and rested horizontallyon the ice surface until 12 August 2010. For this time interval,only surface height and air pressure data are available fromthis station. However, a near-linear relationship between themeteorological data of AWS1, AWS2 and an AWS at the NamCo station (Fig. 1) allowed us to linearly interpolatetemperature, relative humidity, wind speed and globalradiation for this data gap using data from AWS1 and theNam Co AWS. Sonic ranging sensor connectivity problemsresulted in two gaps in the surface height data in 2011(22 March–20 April and 21 May–28 June).

Because of the gentle slope and small distance from thegauge site to AWS2, the topographic effects of precipitationwere neglected. The data from the rain gauge were useddirectly as the precipitation amount for the AWS2 site. Forthe period before the rain gauge was operational, dailyprecipitation amounts were deduced from sonic rangingdata with a snowpack density value of 400 kgm–3 (averageobserved values from snow pit) during the winter from

Fig. 1. Location of Zhadang glacier and the AWSs. Glacier contours are from a 1970 topographic map and the glacier outline is from aLandsat image recorded in 2007.

Table 1. Overview of AWSs and rain gauge instruments and theirspecifications

Sensor type Parameter Accuracy

Campbell CS215 Air temperature �0.48C (5–408C), �0.98C(–408C to +408C)

Relative humidity �2%(10–90% relative humidity)

Young 05103 Wind speed �0.3m s–1

Wind direction �38T. Friedrichs and Co.DPI740

Air pressure �400Pa

Campbell CS300 Solar radiation(incoming and

reflected)

�5% for daily totals

Apogee IRTS-P Surface temperature �0.38C from 58C to 458CCampbell 107TP Ice temperature �0.98C from –358C to +508CCampbell NR-Lite Net all-wave

radiation�5% typical

(�10% worst case)Campbell SR50 Surface height �0.01mGeonor T200B Precipitation �0.6mm

Zhang and others: Energy and mass balance of Zhadang glacier138

4 October 2009 to 20 May 2010 and the densificationprocess of snowpack was not considered here.

CLIMATE CONDITIONS AT THE STUDY SITEThe Nyainqentanglha mountain region is affected by both theIndian summer monsoon and westerlies during winter(Yatagai and Yasunari, 1998), producing distinct seasonaloscillation of the climate. Summer is associated with intensesolar heating and moisture transported by the Indianmonsoon. In contrast, low sun elevation and strong wester-lies cause cold dry windy winters. Figure 2 shows meteoro-logical parameters for Zhadang glacier for the twomass-balance years that were used as the input data for themodel. Daily mean temperature changed markedly with theseasons, with a range of –22.18C to 5.88C. From late May toSeptember, daily temperatures generally rose above 08C atthe study site. Relative humidity and precipitation alsoshowed seasonal variation. Because of the high atmospherictransmissivity on the TP, incoming solar radiation can reach88% of the extraterrestrial solar radiation value. Wind alsovaried seasonally: in summer, the wind speed neverexceeded 10m s–1 and the wind direction was predomin-antly from the southeast; whereas in winter, wind was muchstronger and came predominantly from the northwest (Fig. 3).From the observation at the Nam Co station, >90% of theprecipitation was delivered between May and September in2005/06 (You and others, 2007). May to September isconsidered the wet season and the corresponding dry season

is from October to April. The accumulation and ablationseasons of the glacier overlap in summer (Kang and others,2009). Glaciers in this region are therefore defined assummer-accumulation-type glaciers (SAT glaciers) (Agetaand Higuchi, 1984), the mass balance of which is consideredto be more sensitive to temperature change than that ofwinter-accumulation-type glaciers (Fujita, 2008).

SURFACE ENERGY- AND MASS-BALANCE MODELEnergy balance at the glacier surface can be expressed as

Sin þ Sout þ Lin þ Lout þHS þHL þG �Q ¼ 0 ð1Þwhere Sin is incoming shortwave or global radiation, Sout isreflected shortwave radiation, Lin is incoming longwaveradiation, Lout is outgoing longwave radiation, HS is turbu-lent sensible heat flux, HL is turbulent latent heat flux, G issubsurface heat flux and Q is heat flux for melting. Energyfluxes are defined as positive when directed toward theglacier surface and negative when directed away from thesurface. Thus Eqn (1) can be expressed as

Snet þ Lnet þHS þHL þG ¼ Q ð2Þwhere Snet is net shortwave radiation (Snet = Sin� (1 –�)) andLnet is net longwave radiation (Lin + Lout).

Surface albedo (�=–Sout/Sin) is a critical factor in themass balance of a glacier surface (Van de Wal and others,1992). Considering their dramatically different effects onalbedo, snow and ice surfaces are treated individually in thismodel. Although there are many methods to quantify snow

Fig. 2. Daily mean values of (a) air temperature, (b) wind speed, (c) relative humidity, (d) global solar radiation and (e) precipitation atZhadang glacier during the study period from 4 October 2009 to 15 September 2011. Dashed line in (d) indicates calculated extraterrestrialsolar irradiance. (OND = October to December, etc.)

Zhang and others: Energy and mass balance of Zhadang glacier 139

albedo (Brock and others, 2000), most define albedo as ahigh constant value when significant snowfall occurs and asteadily decreasing value with time after snowfall (e.g. USArmy Corps of Engineers, 1956; Oerlemans and Knap,1998). The problem with this approach is that it yields largediscrepancies between measured and modelled albedoduring prolonged periods without snowfall (Hock andHolmgren, 2005).

The parameterization of snow-surface albedo in themodel used in the present study followed the method ofYamazaki and others (1993), which evaluates surface albedobased on surface snow density, taking into account multiplereflections in the surface snow layer and assuming that eachsuch layer consists of an ice plate and an air layer in thevertical dimension. This parameterization method alsoconsidered the influence of water and the progress ofcompactive viscosity as shown by Fujita and Ageta (2000).Ice-surface albedo was assumed to vary as a function ofdew-point temperature (Molg and others, 2008).

The contribution of incoming longwave radiation toenergy balance was calculated using standard meteoro-logical variables. A key point is the parameterization ofatmospheric emissivity (Crawford and Duchon, 1999).Brutsaert (1975) developed a physically rigorous formulato express the relationship between atmospheric emissivity(") and meteorological parameters as

" ¼ ð1� clfÞ þ clf � 1:24� ðe=T Þ1=7 ð3Þwhere clf is the ratio of the measured incoming shortwaveradiation to the incoming shortwave radiation at the top ofthe atmosphere, and T and e are the air temperature andvapour pressure, respectively. Sicart and others (2010)pointed out that the parameterization performed better fordaily than for hourly simulations. Therefore, the averagedaytime clf was used to calculate daily Lin. Thus the amountof incoming longwave radiation can be expressed as

Lin ¼ �"T 4 ð4Þwhere � is the Stefan–Boltzmann constant.

Lout was obtained by the Stefan–Boltzmann law frommodelled surface temperature and surface emissivity (beingset to 1).

Turbulent sensible (HS) and latent heat fluxes (HL) werecalculated by the bulk aerodynamic method. The gradientsof mean horizontal wind speed (U), mean air temperature (T)and mean specific humidity (q) were assumed to be equal to

the finite difference between the measurement level and thesurface. The turbulent fluxes were expressed as

HS ¼ �CPUCSðT � TsÞ ð5ÞHL ¼ �lf UCLðq � qsÞ ð6Þ

where � is air density, CP is the specific heat capacity of air, Tis air temperature, Ts is surface temperature, qs is specifichumidity at the surface, U is wind speed, lf is latent heat ofevaporation (2.514�106 J kg–1) or sublimation (2.849�106 J kg–1), which are used based on surface temperature,and CS and CL are the bulk exchange coefficients forsensible and latent heat, respectively. Constant bulkexchange coefficients (CS =CL = 0.002; Kondo and Yama-zawa, 1986) were used to calculate the turbulent heat flux asrecommended by Fujita and Ageta (2000) and Sakai andothers (2009) because surface roughness and wind profilesare unknown over snow and ice in this case.

Total energy flux in the subsurface consists of the energyflux from penetrating shortwave radiation together withconductive heat flux. The former was calculated as anexponential decline of net shortwave radiation with in-creasing depth from the surface and it is assumed that theextinction coefficient is a constant value (40m–1) for bothsnow and ice and independent of snow density, grain size,wavelength or other properties (Fukami and others, 1985).Fukami and others (1985) pointed out that the thermalinfluence of solar radiation occurs almost entirely above adepth of 0.1m in the extinction coefficient range 20–100m–1. The conductive heat flux in the subsurface wasexpressed according to the temperature profiles during agiven time-span:

G ¼ K@T@t

Ks ¼ 0:029ð1þ 10�4�2s ÞKi ¼ 488:2

273:2þ TZþ 0:47

ð7Þ

where K is thermal conductivity, of which different valuesare used for snow (Ks) and ice (Ki). In this model, Ks wascalculated as a function of snow density following Mellor(1977), whereas Ki was obtained as a function of icetemperature (Hobbs, 1974).

Surface temperature (Ts) is a key variable for the glaciersurface energy balance. It is calculated using an iterativeprocedure from the energy available at the surface (Andreas,

Fig. 3. Wind direction and intensity of half-hourly observational data at AWS2 for summer and winter (summer: 1 May–30 September 2010and 1 May–15 September 2011; winter: 4 October 2009 to 30 April 2010 and 1 October 2010 to 30 April 2011).

Zhang and others: Energy and mass balance of Zhadang glacier140

1987; Fujita and Ageta, 2000; Fujita and others, 2007). If Tsexceeds the melting point, it is set to 273.15K and theremaining flux represents the heat flux for melting (Q).

Refreezing water in the subsurface was also considered.Refreezing may take place in a range of englacial andsupraglacial locations. Refreezing takes place in the snowlayer when percolating early summer meltwater refreezes inthe cold snow layer and in the capillary water stored in snowpore spaces at the end of summer (Braithwaite and others,1994; Fujita and others, 1996; Schneider and Jansson,2004). Because of the presence of cold ice below the snowlayer, meltwater can also refreeze to form superimposed iceat the interface between snow and ice layers (Marsh andWoo, 1984; Pfeffer and Humphrey, 1996). It was assumedthat the snow layer can retain 5% of its volume as water(Wretain) (Fujita and Ageta, 2000). The amount of refrozenwater (RW) was calculated from the temperature profile ofsnow and ice as follows:

dry cold snow layer: RW ¼ �sCi

lf

Z interface

surface�Ti dz ð8Þ

wet snow layer: RW ¼ min�iCi

lf

Z z

interface�Ti dz,Wretain

� �

ð9Þ

interface of snow and ice layers: RW ¼ �iCi

lf

Z z

interface�Ti dz

ð10Þwhere Ci is the specific heat of ice, lf is the latent heat ofmelting, z is the depth where the energy fluxes become nil,and �s and �i are the density of snow and ice, respectively.

Precipitation at high altitudes occurs as solid (snowfall),liquid (rainfall) and mixed phases (Kayastha and others,1999). The proportion of snowfall versus rain is governed bythe wet-bulb temperature TW (Yamazaki, 2001). The follow-ing equations are proposed for the fraction ([0,1]) of snowfall(Ps) in the total precipitation (Pp):

Ps ¼ 1� 0:5 exp ð�2:2ð1:1� TWÞ1:3Þ TW < 1:1�C

Ps ¼ 0:5 exp ð�2:2ðTW � 1:1Þ1:3Þ TW � 1:1�C

and the amount of rainfall is expressed as

Pr ¼ Ppð1� PsÞ ð11ÞWet-bulb temperature, TW, can be calculated as

TW ¼ ðB � Ta þ e � 6:086Þð0:476þ BÞ ð12Þ

B=0.0006336�p, where Ta is air temperature (8C), e iswater vapour pressure (hPa) and p is air pressure (hPa).

VALIDATION OF THE MODELA set of observed daily data (air temperature, relativehumidity, wind speed, incoming shortwave radiation andprecipitation) from 4 October 2009 to 15 September 2011was used as input data to run the energy-balance model. Thesnow thickness and average ice temperature recorded on4 October 2009 were used as the initial conditions.Validation of the model results against the measured datawas undertaken as described below.

Comparisons of observed and calculated variables forAWS2 (Fig. 4) indicate that the modelled surface albedovalues are similar to the observed values (Fig. 4a). Since a

constant value was used for snow density (mean values ofthe field observations: 400 kgm–3), the modelled albedo hadalmost the same value even after a significant snowfall,which caused a small discrepancy between the observedand modelled values. The observed albedo values were bothlower than calculated in early June 2010 and early July2011. This may be due to the deposition of dust in thebeginning of the melt season (Fujita and Ageta, 2000; Fujita,2007), which was not considered in the model. However,the results of the modelled snow surface albedo aregenerally acceptable. In this study, the ice albedo varied asa function of dew-point temperature, which strongly affectsice surface albedo (Molg and others, 2008). Since obser-vations of albedo data in summer 2010 are lacking, thismethod could only be validated through mass-balanceresults because observed changes of surface level duringthe period were affected by the data gap. Although Lin wasnot measured directly by AWS2, it was calculated as aresidual using data from three of the other four componentsof net radiation (Lout was calculated based on measuredsurface temperature). The results show a close correlationbetween the modelled and observed data (Fig. 4b). Figure 4cpresents a comparison of observed and calculated surfacetemperatures. During the data gap in summer 2010, thedaily mean air temperature was always above 08C, and thusthe modelled daily surface temperature was 08C. Variationsin snow depth and the amount of melting ice (which has adensity of 900 kgm–3) were also validated by observedsurface level data (Fig. 4d). The modelled results agree wellwith the observed values, thereby confirming the low valuefor ice-surface albedo during the data gap in summer 2010.In general, the model incorporated almost all the energyexchange that took place at the glacier surface andperformed well in calculating these variables.

RESULTSEnergy balanceDaily surface energy components of the energy balance areshown in Figure 5. The energy-balance results indicate thatSnet was highly variable, from a very high average value of92Wm–2 in summer to a low of 46Wm–2 in winter(Table 2). Aside from seasonal changes in sun elevation,the main reason for the seasonal variability of Snet is thevarying glacier surface albedo. The average albedo (0.8)indicates that the snow surface reflected most of Sin duringwinter. In contrast, the lower average albedo (0.65) duringsummer was associated with surface melt. The mean valueof Lnet in summer was –47Wm–2, slightly less than the meanvalue of –59Wm–2 in winter. This difference is related tovariations in Lin and Lout, the two components of Lnet. Thevalue of Lout, which is governed by glacier surface tempera-ture, exhibited regular seasonal changes during the 2 yearsof observations. The value of Lin, depending on atmospherictemperature, cloud cover and humidity, was high in summerand low in winter (Table 3; Fig. 4). Positive HS indicates heattransfers from the air to the glacier surface throughout theyear. The seasonal variation in HS points to a largertemperature gradient in winter than in summer (Table 3).For turbulent HL, a sign shift from negative to positiveoccurred during summer. The relatively high air temperatureand relative humidity (Table 3) leads to a reversal of thehumidity gradient and therefore a positive HL for a meltingvalley glacier (Oerlemans, 2000). The windy conditions

Zhang and others: Energy and mass balance of Zhadang glacier 141

Fig. 5. Daily mean values of energy-balance components at site AWS2 for 4 October 2009 to 15 September 2011. Snet is net shortwaveradiation, Lnet is net longwave radiation, HS is sensible heat flux, HL is latent heat flux, G is subsurface conductive heat flux and Q is themelting component. (OND = October to December, etc.)

Fig. 4. Observed and modelled daily (a) albedo, (b) incoming longwave radiation, (c) surface temperature and (d) height from the sonicranger sensor to Zhadang glacier surface and their correlation coefficient at the site AWS2 for 4 October 2009 to 15 September 2011. Icealbedo calculated as a function of daily dew-point temperature (TW): –0.05368C–1 TW+0.4681, which was gained from the correlation ofobserved ice albedo and TW during summer 2011. (OND = October to December, etc.)

Zhang and others: Energy and mass balance of Zhadang glacier142

contribute to the larger values of both HS and HL in winterthan in summer. The sign of the subsurface heat flux (G),which shifted from positive to negative, is a function of theannual energy cycle. A positive value for G suggests thatsubsurface cold content accumulated during winter,whereas a negative G implies the release of cold contentin summer. As a result of the energy balance, positive meltheat flux (Q), with almost the same oscillation trend as Snet,occurred only in summer.

Table 4 lists the contributions of energy-flux componentsto total heat flux. For the whole period of observation, theradiation heat flux (|Snet|+|Lnet|) accounted for 82% of thetotal heat flux and was the most important heat-fluxcomponent. Turbulent sensible and latent heat flux followedat 10% and 6%, respectively. The subsurface heat flux (2%)contributed little of the energy-flux components to the total

heat flux throughout the study. These fluxes exhibited thesame order-of-magnitude contribution in both winter andsummer. The main seasonal variation in the energy balanceduring the study period is found in two radiation com-ponents: net shortwave radiation and net longwave radi-ation. During the winter season, Lnet dominated theradiation heat-flux component, but Snet became moreimportant during the summer season.

Glacier mass balanceTable 5 lists the calculated mass-balance components at theAWS2 site. The results show that most of the precipitationoccurred during summer: 80% and 87% in 2010 and 2011,respectively. The minor part of the precipitation that fellduring winter was all in the form of snowfall. Duringsummer, 74% and 85% of the precipitation was in the form

Table 2. Mean seasonal values of energy-flux components (Wm–2)

Energy-flux component 2009/10 2010/11 Winter average Summer average

Winter (Oct–Apr) Summer (May–Sept) Winter (Oct–Apr) Summer (May–Sept)

Sin 200 255 208 274 204 264Sout –155 –148 –162 –197 –159 –172Lin 191 264 187 258 189 261Lout –249 –309 –247 –307 –248 –308Snet 45 107 46 77 46 92Lnet –58 –45 –60 –50 –59 –47HS 22 10 18 8 20 9HL –10 –8 –7 –10 –9 –9G 0 –4 3 –2 2 –3Q 0 61 0 24 0 43

Table 3. Seasonal mean values of meteorological variables

Factor 2009/10 2010/11

Winter (Oct–Apr) Summer (May–Sept) Winter (Oct–Apr) Summer (May–Sept)

Air temperature (8C) –10.2 1.2 –11.4 0.6Relative humidity (%) 34.7 70.4 41.6 69.9Wind speed (m s–1) 3.9 3.1 3.5 3.2Albedo 0.8 0.6 0.8 0.7Cloud coverage* 0.3 0.4 0.3 0.4�T (K){ 5.8 2.7 5.1 2.5

*Cloud coverage was calculated as (1 – clf)/(clfmax – clfmin)� 100% where clf is the ratio of the measured incoming shortwave radiation to the incomingshortwave radiation at the top of the atmosphere, and clfmin and clfmax are the calculated minimum and maximum values of clf within the study period,respectively.{Denotes the difference between air temperature and surface temperature.

Table 4. Seasonal energy fluxes at the glacier surface and proportional contribution of each flux

Mass-balance year Season Sum* Snet Lnet HS HL G

Wm–2 % % % % %

2009/10 Winter 136 33 42 16 8 0Summer 173 62 26 6 4 2

2010/11 Winter 134 35 45 13 5 2Summer 147 52 34 6 7 2

All observed periods – 148 45 37 10 6 2

*Sum is the sum of the energy fluxes in absolute values: |Snet|+|Lnet|+|HS|+|HL|+|G|; proportional contribution of each flux was calculated as |energy flux|/sum.

Zhang and others: Energy and mass balance of Zhadang glacier 143

of snow in 2010 and 2011, respectively. Because of strongmelting in summer, nearly all of the penetration water(rainfall and meltwater) ran off as discharge and only a smallamount (117mmw.e. in 2010 and 104mmw.e. in 2011)was refrozen as superimposed ice. Seasonal variations inevaporation (sublimation) during the study period weresubtle (average value of 100mmw.e. for the 2 years).Although the mass balance was positive in both winters, thelarge mass deficits in summer resulted in negative annualmass balances of –1968 and –432mmw.e., respectively, forthe two years at this site.

DISCUSSION

Sensitivity of mass balance to meteorologicalvariablesIn order to test the sensitivity of mass balance to meteoro-logical variables, test cases were prescribed. Here wealtered the air temperature by �18C, relative humidity by�20% and precipitation by �20% throughout the period.The mass-balance change then reflects its sensitivity to theperturbation of variables. As shown in Figure 6, 2.04mw.e.more meltwater (an increase of 85%) would run off at theobservation site if the air temperature was increased by 1K,

while 0.69mw.e. (29%) of snow or ice would melt if airtemperature was decreased by 1K. Air temperature, as akey factor, will particularly control when melt commencesand how fast the winter snowpack is removed. Since lowerice albedo will amplify ablation (Andreassen and others,2008), increasing temperature will not only increase iceablation but also prolong the melt season. Thus massbalance is more affected by an air temperature perturbationof +1K than by a perturbation of –1K, especially in theablation area of the glacier.

The mass-balance changes for perturbations of relativehumidity (RH) are –1.3mw.e. (55%) and 0.68mw.e. (29%)for +20% and –20% humidity perturbations, respectively.Previous studies also show the sensitivity of glacier massbalance to changes in moisture (Wagnon and others, 1999,2001; Francou and others, 2003; Molg and others, 2003). Anincrease of 20% in precipitation directly influences theamount of accumulation, but also changes the albedo andthus the melting. More snowfall increases surface albedo andreduces the main energy source (net shortwave radiation),leading to less ablation (Molg and others, 2008). Thesensitivity to a �20% change in precipitation is higher thanfor a 1K change in temperature. The results show that themodel is nearly twice as sensitive to a 20% change inprecipitation as to a 20% change in relative humidity.

Table 5. Calculated annual and seasonal mass-balance components at site AWS2: mass balance =precipitation – runoff – evaporation;runoff = rainfall +meltwater – refrozen water (mmw.e.)

Mass-balance component 2009/10 2010/11 2009/10 2010/11

Winter (Oct–Apr) Summer (May–Sept) Winter (Oct–Apr) Summer (May–Sept)

Precipitation 112 456 64 423 568 487Rainfall 0 118 0 63 118 63Snowfall 112 338 64 360 450 424Meltwater 0 2427 0 867 2427 867Refrozen water 0 117 0 104 117 104Runoff 0 2428 0 826 2428 826Evaporation 69 40 46 46 109 92Mass balance 43 –2012 18 –449 –1969 –431

Fig. 6. The sensitivity of specific mass balance was examined by perturbations of temperature (�1K), relative humidity (�20%) andprecipitation (�20%). The results show that the specific mass balance is more sensitive to changes in precipitation than other variables.

Zhang and others: Energy and mass balance of Zhadang glacier144

Typical features of the energy and mass balance onZhadang glacierZhadang glacier is subject to particular seasonal climaticconditions that induce seasonal circumstances of energy andmass balance. In winter, negative Lnet, the dominantradiation component, caused net radiation to be negative.This part of the energy sink was compensated by positiveturbulent heat flux (HS +HL) and subsurface heat flux G.Thus, no melting occurred in winter. The sign of HL

(negative) indicates that the only mass loss during winterwas in the form of sublimation. In summer, positive Snet, themost significant heat flux, together with HS, contributed topositive Q for glacier surface melting. The energy releasedby condensation, positive HL (see Fig. 5), enhanced surfacemelting during midsummer (Oerlemans, 2000; Giesen andothers, 2008, 2009). As a result, strong summertime meltingoccurred on the glacier surface in the ablation zone.

Changes in summer climates and their influence onmass balanceThe monthly frequency, total amount and form of precipi-tation during the summer (May–October) are shown inFigure 7. According to Chang and Chen (1995), the warmwet airflow of the Indian monsoon begins in mid-June,which is thus the beginning of the precipitation season. Theprecipitation monthly distribution implied that the Indianmonsoon started a month later than usual in 2010. Incontrast, the precipitation increased dramatically in June2011, indicating that the Indian monsoon invaded theregion. Subsequently, the monsoon became strongest withthe highest rate of precipitation in July, followed by aweakening in August. Yang and others (2011) reported thatglacier surface energy- and mass-balance variations wererelated to the progress of the Indian monsoon during themelting season in southeast Tibet. Monthly mean values ofenergy-balance components and mass balance are pre-sented in Figure 8 and Table 6, respectively. In May 2010and 2011, the energy input as net radiation and HS wereentirely consumed by HL (sublimation) and G (as cold

content release) and therefore no melting occurred. Allsnowfall contributed to mass accumulation. Thus, positivemass balance was shown on the glacier surface (also shownby the variation in snow depth in Fig. 9). With increasing sunelevation and air temperature in June, positive Q emergedon the glacier surface at the beginning of the melting season.In June 2010, a large amount of net shortwave radiation(71Wm–2) was available for melting on the glacier surfacedue to early exposure of the ice surface (Fig. 9). In contrast,intense snowfall ensured that the glacier surface wascovered with snow (albedo=0.8) in June 2011. The snowsurface reflected most of Sin, and as a result only a smallamount became melt heat flux Q (8Wm–2). Therefore,distinctly different mass-balance results were found in thetwo years: –452mmw.e. in June 2010 and 98mmw.e. inJune 2011. In July 2010, with increasing air temperature, theamount of snowfall was small. Thus, the ice-dominatedglacier surface (average albedo of 0.3) absorbed most of Sin,and strong melting (Q =141Wm–2) occurred on the surface,causing a huge mass deficit of –1076mmw.e. In July 2011,the thin snow layer (�=0.7) from frequent snowfall kept Snetat a low level and resulted in a low melting rate on thesurface (Q=46Wm–2) and a consequent mass-balanceresult of –258mmw.e. In August 2010, precipitationreached its highest amount. Although nearly half of theprecipitation was rainfall, snowfall still kept the surface at arelatively high albedo (0.5) and resulted in a large amount ofSnet (Snet = 109Wm–2). Cloudy conditions (clf = 61.5%) alsoenhanced Lin and provided a positive effect for melting.Furthermore, the positive HL at the beginning of August(Fig. 5) also made a positive contribution to surface melting.As a result, there was still a large melt heat flux (84Wm–2),which resulted in a mass balance of –542mmw.e. duringAugust 2010. In August 2011, due to less snowfall, a low-albedo surface (0.6) absorbed the largest amount of Sin(Snet = 108Wm–2) compared with former months and alsoled to the largest net radiation (57Wm–2). However,evaporation was also largest at this time and shared–17Wm–2 of heat flux going into evaporation. The outcome

Fig. 7. The monthly amount, form and frequency of precipitation in the summers of 2010 and 2011. Frequency was calculated as the numberof daily precipitation events per month.

Zhang and others: Energy and mass balance of Zhadang glacier 145

of the energy balance was a 44Wm–2 heat flux available formelting and a mass balance of –292mmw.e. during August2011. The small positive mass balance in September markedthe end of the melt season for that year.

Although the precipitation sum was almost the same inboth summers (456mmw.e. in 2010 and 423mmw.e. in2011) there was a distinct mass-balance difference betweenthe summers of 2010 (–2011mmw.e.) and 2011 (–449mmw.e.). Fujita (2000) pointed out that some precipitation (rain)fails to contribute to the accumulation, but snowfall keeps thealbedo high and largely limits ablation during themelt seasonon SAT glaciers. Thus, SAT glaciers are more vulnerable thanwinter-accumulation-type glaciers. This is because the in-crease in air temperature causes a decrease in accumulationand a drastic increase in ablation with lowering albedo. Thiswas the situation on Zhadang glacier during the summer of2010. A study on Glaciar Zongo, Bolivia (Sicart and others,2011), suggests that melt is reduced by snowfall during thewet season via the albedo effect during the melt season. Wethus conclude that SAT glaciers are very sensitive tovariations of precipitation seasonality (or monthly distri-bution) and form (proportion of snowfall and rainfall) assuggested by previous studies (e.g. Kang and others, 2009).

CONCLUSIONSA physically based energy-balance model with forcing dataincluding air temperature, humidity, wind speed, globalradiation and precipitation was used to calculate the surfaceenergy balance at site AWS2 on Zhadang glacier over

2 years. The calculated surface albedo, incoming longwaveradiation, surface temperature and surface height corres-ponded well with observed values. The results indicate thatthe model is reliable enough to make robust calculations ofsurface energy and mass balance. For the whole observationperiod, the radiation component dominated (82%) the totalsurface energy heat fluxes. Turbulent sensible (10%) andturbulent latent heat flux (6%) followed. Subsurface heat fluxrepresented a very minor proportion (2%) of the total heatflux. The main seasonal variations in energy fluxes werecaused by changes in net shortwave and longwave radiationand these led to different mass-balance results. In winter,dominant negative net longwave radiation resulted innegative net all-wave radiation. This energy sink was offsetby positive turbulent and subsurface heat fluxes, and no meltoccurred in winter. In summer, net shortwave radiation wasthe most important radiation component and causedpositive net radiation. The positive radiation heat flux,together with positive turbulent heat flux, provided the meltheat flux for surface melting. The dramatic differences insummer mass balance between 2010 and 2011 indicate thatthe glacier surface mass balance was closely related toprecipitation seasonality and form. The present studysuggests that glacier mass-balance models that use annualvariations as input factors, rather than seasonal or monthlyvariations, may err significantly in their estimates of mass-balance variability on SAT glaciers. To better describe theevolution of summer-accumulation glacier surface, hightime resolution precipitation data are necessary during thecalculation of glacier surface mass balance.

Table 6. Monthly mean values of meteorological factors, melt heat flux and mass balance during summer

Air temperature Relative humidity Cloud coverage Albedo Q Mass balance

2010 2011 2010 2011 2010 2011 2010 2011 2010 2011 2010 2011

8C 8C % % % % Wm–2 Wm–2 mmw.e. mmw.e.

May –2.8 –2.7 62.5 59.4 44.5 34.8 0.8 0.8 0 0 34 33June 1.9 0.8 62.0 71.5 41.8 44.6 0.6 0.8 71 8 –452 98July 3.2 2.4 75.7 81.4 55.0 58.0 0.3 0.7 141 46 –1076 –258Aug 2.9 1.5 79.6 70.3 61.5 53.0 0.5 0.6 84 44 –542 –292Sept* 0.9 1.5 71.8 63.4 47.0 44.4 0.7 0.7 8 16 25 –31

*For the interval 1–15 September 2011.

Fig. 8. Monthly mean energy components of the glacier surface for summer (September 2011: for the interval 1–15 September).

Zhang and others: Energy and mass balance of Zhadang glacier146

ACKNOWLEDGEMENTSThis work is supported by the Global Change ResearchProgram of China (2010CB951401), the National NaturalScience Foundation of China (41190081, 41225002) andthe German Research Foundation (DFG) within the TibetanPlateau Priority Programme (TiP) (SCHE 750/4-1, SCHN 680/3-1 and BU 949/20-1). We thank colleagues working atNam Co station.

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MS received 10 August 2012 and accepted in revised form 2 November 2012

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